To unlock the Target Eliminated trophy in Mortal Kombat 11, you will need to perform two Fatalities with Sonya Blade.
Obviously, this will be easier against a second controller or against the CPU on Very Easy difficulty. You can also speed this up by setting the "Rounds to win" to one instead of two.
Once you win the fight and see the "Finish Him/Her", perform the two Fatalities below:
Fatality One: (Mid Distance) Down > Forward > Back >
Fatality Two: (Close) Back > Forward > Down >